Hypercube (EntityClass, 17)

(Difference between revisions)

Revision as of 20:06, 15 June 2007

A hypercube is an n-dimensional analog to a cube. Hypercubes include the point, line, square, cube and tesseract.

		Dimension of hypercube						Formula
		0	1	2	3	4	5	Formula
http://invhost.com/share/dimhyc_rotated.png	0	1	2	4	8	16	32	2ⁿ
	1	0	1	4	12	32	80	n2^n-1
	2	0	0	1	6	24	80	n(n-1)2^n-22^-1
	3	0	0	0	1	8	40	n(n-1)(n-2)2^n-36^-1
	4	0	0	0	0	1	10	n(n-1)(n-2)(n-3)2^n-424^-1
	5	0	0	0	0	0	1	n/a
	Sum	1	3	9	27	81	243	3ⁿ

Number of k-cubes in an n-cube: 2^n-kn!/(k!(n-k!))